RIO DE JANEIRO — In the campaign against mosquitoes, Brazil has deployed soldiers to destroy habitats where the insects thrive. Colombia is releasing swarms of mosquitoes treated with bacteria that limit their capacity to spread disease. Mexico is testing the first vaccine against dengue fever, a mosquito-borne virus raging throughout the region.

Yet at each turn, mosquitoes are outwitting their human opponents, a challenge highlighted by the United States’ decision to advise pregnant women to postpone traveling to more than a dozen Latin American or Caribbean countries and Puerto Rico where mosquitoes are rapidly expanding the reach of Zika, the virus linked to a surge in cases of infants born with brain damage.

The warning by the Centers for Disease Control and Prevention in Atlanta has intensified a debate across Latin America over the hemisphere’s growing vulnerability to mosquito-borne diseases. These concerns are especially acute in Brazil, the region’s largest country, where officials hope that tourism can help revive a beleaguered economy as they prepare to host the 2016 Summer Olympics in Rio de Janeiro.

Henrique Alves, Brazil’s tourism minister, took issue with the C.D.C.’s warning on Saturday. He argued that the Brazilian authorities were adopting measures to prevent Zika from intensifying in the country, even though health officials were investigating more than 3,500 cases of microcephaly, a previously rare condition linked to Zika in which infants are born with abnormally small heads.

Asked in a telephone interview if Brazil was a safe destination for pregnant women, Mr. Alves responded, “I think so, without a doubt,” emphasizing that his government’s decision to refrain from travel alerts regarding Zika coincided with World Health Organization policies.

Mr. Alves added that he expected the Zika outbreak to ease to the point that the Olympics here in August would not be affected.

Yet others in Brazil applauded the C.D.C.’s alert, pointing to the country’s struggle not just with Zika, a virus with origins in Uganda that is thought to have made the leap to Brazil in 2014, but also with two other mosquito-borne viruses, dengue and chikungunya. Last year, Brazil registered more than 1.6 million cases of dengue, a virus causing fever and joint pain, with 863 people dying from the disease.

“The announcement by the C.D.C. is entirely appropriate, given the risks in Brazil,” said Dr. Artur Timerman, 62, an infectious disease specialist in São Paulo.

He said that he had advised his own daughter, who is 32, to avoid getting pregnant now in Brazil. “If she wants to do so, her best course of action is to leave the country and go to a place where Zika is not a problem,” he said.

Those infected with Zika usually experience mild or no symptoms. It is not known whether the virus alone causes microcephaly or if it occurs only if the mother has had a previous infection, like dengue.

Zika has emerged as a health threat elsewhere in Latin America. In El Salvador, cases of Zika have escalated since it was first reported at the end of November. As of last week, 3,836 cases had been reported, and the government raised the alert level in 47 municipalities where the illness had been detected. The government is planning intensive fumigation campaigns in those areas.

El Salvador’s Health Ministry is particularly concerned about the rise of cases of Guillain-Barré syndrome, which leads to paralysis, usually temporary; researchers are exploring a possible link between Guillain-Barré and Zika. Forty-six suspected cases of the syndrome had been reported as of last week, Violeta Menjívar, the health minister, said in a radio interview.

Dr. Pablo Kuri Morales, Mexico’s undersecretary for Prevention and Health Promotion, said in a telephone interview on Saturday that Mexico had diagnosed 15 cases of Zika, 10 of them in the state of Chiapas, on the border of Guatemala. He added that the authorities were preparing a television and radio campaign to warn everybody, especially women of reproductive age.

Dr. Kuri said the C.D.C. was “within its rights” to issue the travel warning, but he argued that the blanket admonition did not make sense when the virus has appeared in only three Mexican states. The mosquitoes that carry the virus, he said, could not survive in the high altitudes of the central plateau, including Mexico City.

“I think it’s good to have these warnings,” he said, “but these things should be explained to people.”

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Mosquitoes in a São Paulo University lab. Brazil has renewed efforts after the outbreak of Zika, a mosquito-borne virus linked to brain damaged babies.CreditNelson Almeida/Agence France-Presse — Getty Images

In Washington, administration officials said the decision to issue a travel alert on Friday developed quickly at the end of the week and set off a flurry of diplomatic efforts to inform officials in the countries named in the alert.

Officials said the notification process forced the C.D.C. to postpone a news conference that had been planned for Friday afternoon, ultimately delaying an announcement until that evening.

Aside from anecdotal accounts, it seems too early to tell how the alert will affect travel. In Brazil, Olympic officials emphasized that the Games will take place in August, during the Southern Hemisphere’s winter. The dryer, cooler weather around that time is thought to reduce the presence of mosquitoes, though virologists warn that the insects can transmit viruses year-round in Brazil.

“Rio 2016 will continue to monitor the issue closely and follow guidance from the Brazilian Ministry of Health,” said Philip Wilkinson, a spokesman for the committee organizing the Games.

Dr. Isaac I. Bogoch, a tropical infectious disease specialist at the University of Toronto who is part of a team modeling the potential for Zika to spread, warned that the Olympics could serve as a catalyst for the virus, which some researchers believe may have arrived in Brazil during another sports mega-event, the 2014 World Cup.

“There will be people traveling to Brazil from all over the world,” Dr. Bogoch said in an email.

“The concern is that infected individuals will travel back to their home country and introduce the virus to new regions.”

Dr. Bogoch and other researchers determined that Zika had the potential to rapidly spread to other parts of the world, according to findings published last week in the British medical journal The Lancet.

Their model for Zika’s possible spread, using worldwide temperature profiles and air travel routes, also determined that more than 60 percent of the population in the United States lives in areas conducive to seasonal Zika transmission. And about 23 million people in the United States live in places with climates like Florida and parts of Texas where Zika can be transmitted by mosquitoes year-round, the researchers said.

The authorities in Brazil insist that they are taking steps to fight Zika, including vaccine research.